Related papers: Pseudofractal Scale-free Web
We analyse growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and…
We study the average nearest neighbor degree $a(k)$ of vertices with degree $k$. In many real-world networks with power-law degree distribution $a(k)$ falls off in $k$, a property ascribed to the constraint that any two vertices are…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most…
Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free…
In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
We consider a stochastic model for directed scale-free networks following power-laws in the degree distributions in both incoming and outgoing directions. In our model, the number of vertices grow geometrically with time with growth rate p.…
Scale-free networks with moderate edge dependence experience a phase transition between ultrasmall and small world behaviour when the power law exponent passes the critical value of three. Moreover, there are laws of large numbers for the…
In this paper we present a deterministic vertex spawning model that yields a scale-free network. The model specifies that a parent vertex produces a child vertex in a time interval approximately proportional to the current time and…
Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and…
We investigate a growing network model that combines preferential and uniform attachment with two distinct mechanisms of edge deletion. In addition to the usual uniform probability edge deletion, we introduce a novel node-based rule in…
In contrast to the conventional wisdom that scale-free networks are prone to epidemic propagation, in the paper we present that disease spreading is inhibited in fractal scale-free networks. We first propose a novel network model and show…
We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
The degree distribution of a real world network -- the number of links per node -- often follows a power law, with some hubs having many more links than traditional graph generation methods predict. For years, preferential attachment and…
We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant…
While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is…